Indiana Once Tried to Change Pi to 3.2

Any high school geometry student worth his or her protractor knows that pi is an irrational number, but if you’ve got to approximate the famed ratio, 3.14 will work in a pinch. That wasn’t so much the case in late-19th-century Indiana, though. That’s when the state’s legislators tried to pass a bill that legally defined the value of pi as 3.2.

The very notion of legislatively changing a mathematical constant sounds so crazy that it just has to be an urban legend, right? Nope. As unbelievable as it sounds, a bill that would have effectively redefined pi as 3.2 came up before the Indiana legislature in 1897.

The story of the “Indiana pi bill” starts with Edward J. Goodwin, a Solitude, Indiana, physician who spent his free time dabbling in mathematics. Goodwin’s pet obsession was an old problem known as squaring the circle. Since ancient times, mathematicians had theorized that there must be some way to calculate the area of a circle using only a compass and a straightedge. Mathematicians thought that with the help of these tools, they could construct a square that had the exact same area as the circle. Then all one would need to do to find the area of the circle was calculate the area of the square, a simple task.

Sounds like a neat trick. The only problem is that it’s impossible to calculate the area of a circle in this way. It just won’t work. Furthermore, when Goodwin was toying with this problem, mathematicians already knew it was impossible; Ferdinand von Lindemann had proven that the task was a fool’s errand in 1882.

Goodwin wasn’t going to let something trivial like the proven mathematical impossibility of his task deter his efforts, though. He persevered, and in 1894 he even convinced the upstart journal American Mathematical Monthly to print the proof in which he “solved” the squaring-the-circle problem. Goodwin’s proof didn’t explicitly deal with approximating pi, but when you’re quite literally trying to fit a square peg in a round hole, weird things happen. One of the odd side effects of Goodwin’s machinations was that the value of pi morphed into 3.2.

Let's Make a Deal

Although Goodwin’s “proof” was anything but, he was pretty cocky about its infallibility. He didn’t just publish his faulty method in journals; he copyrighted it. Goodwin figured everyone would be lining up to use his revolutionary new trick, and his plan was to collect royalties from businesses and mathematicians who sought to exploit his method.

Goodwin wasn’t totally greedy, though, and that’s where the Indiana legislature entered the picture. Goodwin couldn’t bear the thought of Hoosier schoolchildren being deprived of the fruits of his brilliance just because the state couldn’t foot the bill for his royalties. So he magnanimously offered to let the state use his masterpiece free of charge.

Indiana wasn’t going to get such an awesome deal totally for free, though. The state could avoid paying royalties if and only if the legislature would accept and adopt this “new mathematical truth” as state law. Goodwin convinced Representative Taylor I. Record to introduce House Bill 246, which outlined both this bargain and the basics of his method.

Again, Goodwin’s method and the accompanying bill never mention the word “pi,” but on the topic of circles, it clearly states, “[T]he ratio of the diameter and circumference is as five-fourths to four.” Yup, that ratio is 3.2. Goodwin isn’t afraid to lambaste the old approximation of pi, either. The bill angrily condemns 3.14 as “wholly wanting and misleading in its practical applications.”

Goodwin’s blasting of the old approximation isn’t even the funniest part of the bill’s text. The third and final section extols his other mathematical breakthroughs, including solving the similarly impossible problems of angle trisection and doubling the cube, before reminding any reader who wasn’t sufficiently awestruck at his magnificence, “And be it remembered that these noted problems had been long since given up by scientific bodies as insolvable mysteries and above man's ability to comprehend.“

Math Problem

To anyone who passed the aforementioned high school geometry class, this bill was patently absurd. Apparently Indiana legislators weren’t a pack of math whizzes, though. After the bill bounced around between committees, the Committee on Education finally sent it out for a vote, and the bill passed the House unanimously. No, not a single one of Indiana’s 67 House members raised an eyebrow at a proof that effectively redefined pi as 3.2.

Luckily the state’s senators had a bit more numerical acumen. Well, some of them did. Eventually. After sailing through the House, the bill first went to the Senate’s Committee on Temperance, which also recommended that it pass. By this point, news of Indiana attempting to legislate a new value of pi and endorse an airtight solution to an unsolvable math problem had become national news, and papers all over the country were mocking the legislature’s questionable calculations.

All this attention ended up working in Indiana’s favor. While the state’s lawmakers couldn’t follow Goodwin’s bizarre brand of mathe-magic well enough to refute his proof, there were other smart Hoosiers who could. Professor C.A. Waldo of Purdue University was in Indianapolis while the pi hoopla was unfolding, and after watching part of the debate at the statehouse he was so thoroughly horrified that he decided to intervene.

The legislators may have been nearly bamboozled by Goodwin’s pseudo-math, but Waldo certainly wasn’t. Waldo got the ear of a group of senators after watching the absurd debate and explained why Goodwin’s theory was nonsense. (It seemed that most of the legislators didn’t really understand what was going on in the bill; they just knew that by approving it the state would get to use a new theory for free.)

After receiving Waldo’s coaching, the Senate realized that the new bill was a very, very bad idea. Senator Orrin Hubbel moved that a vote on the bill be postponed indefinitely, and Goodwin’s new math died a quiet legislative death. The Indiana legislature hasn’t tried to rewrite the basic principles of math in all the years since.

Happy Pi Day! For decades, math lovers have been honoring this crucial irrational constant on March 14 (or 3/14, the first three digits of the ratio of a circle's circumference to its diameter) every year. The U.S. House of Representatives even passed a non-binding resolution in 2009 to recognize the date. Join the celebration by solving (or at least puzzling over) these problems from a varied collection of pi enthusiasts.

PI IN SPACE

iStock

Pi is a vital number for NASA engineers, who use it to calculate everything from trajectories of spacecraft to densities of space objects. NASA's Jet Propulsion Laboratory, located in Pasadena, California, has celebrated Pi Day for a few years with a Pi in the Sky challenge, which gives non rocket engineers a chance to solve the problems they solve every day. The following problems are from Pi in the Sky 3 (and you can find more thorough solutions and tips there). JPL has brand-new problems for this year's event, Pi in the Sky 5.

1. HAZY HALO

This undated NASA handout shows Saturn's moon, Titan, in ultraviolet and infrared wavelengths. The Cassini spacecraft took the image while on its mission to gather information on Saturn, its rings, atmosphere and moons. The different colors represent various atmospheric content on Titan.

NASA, Getty Images

Given that Saturn's moon Titan has a radius of 2575 kilometers, which is covered by a 600-kilometer atmosphere, what percentage of the moon's volume is atmospheric haze? Also, if scientists hope to create a global map of Titan's surface, what is the surface area that a future spacecraft would have to map?

[Answer: 47 percent; 83,322,891 square kilometers]

2. ROUND RECON

NASA's Earth-orbiting Hubble Space Telescope took this picture June 26, 2003 of Mars.

NASA, Getty Images

Given that Mars has a polar diameter of 6752 kilometers, and the Mars Reconnaissance Orbiter comes as close to the planet as 255 kilometers at the south pole and 320 kilometers at the north pole, how far does MRO travel in one orbit? (JPL advises, "MRO's orbit is near enough to circular that the formulas for circles can be used.")

[Answer: 23,018 km]

3. SUN SCREEN

In this handout provided by NASA, the planet Mercury is seen in silhouette, lower left of image, as it transits across the face of the sun on May 9, 2016 as viewed from Boyertown, Pennsylvania. Mercury passes between Earth and the sun only about 13 times a century, with the previous transit taking place in 2006.

PUTTING THE PI IN PIZZA

iStock

People often celebrate Pi Day by eating pie, but what is considered a "pie" is subjective. Pizza Hut considers its main offerings pies, and got into the spirit of Pi Day in 2016 by asking their customers to solve several math problems from English mathematician and Princeton professor John Conway, with promises of free pizza for winners for 3.14 years. Below are two of his fiendishly tricky problems. Unfortunately, even if you solve them, your chance at free pizza is long gone.

4. 10-DIGIT GUESS

iStock

I'm thinking of a 10-digit integer whose digits are all distinct. It happens that the number formed by the first n of them is divisible by n for each n from 1 to 10. What is my number?

[Answer: 3,816,547,290]

5. PUZZLE CLUB

iStock

Our school's puzzle club meets in one of the classrooms every Friday after school.

Last Friday, one of the members said, "I've hidden a list of numbers in this envelope that add up to the number of this room." A girl said, "That's obviously not enough information to determine the number of the room. If you told us the number of numbers in the envelope and their product, would that be enough to work them all out?"

He (after scribbling for some time): "No." She (after scribbling for some more time): "Well, at least I've worked out their product."

What is the number of the school room we meet in?

[Answer: Room #12 (The numbers in the envelope are either: 6222 or 4431, which both add up to 12 and the product is 48.)]

COM-PI-TITIVE MATH

iStock

Po-Shen Loh coached the U.S. Mathematical Olympiad team to victory in 2015 and 2016. The back-to-back win was particularly impressive considering Team USA had not won the International Mathematical Olympiad (or IMO) in 21 years. When not coaching, Loh is an associate math professor at Carnegie Mellon University. His website, Expii, challenges readers weekly with a large range of problems. Expii has celebrated Pi Day for several years now—this year it published a video that uses an actual pie to help us visualize pi better—and the following problems are from its past challenges.

6. PIESTIMATE

iStock

Pi has long been noted as one of the most useful mathematical constants. Yet, due to the fact that it is an irrational number, it can never be expressed exactly as a fraction, and its decimal representation never ends. We have come to estimate π often, and all of these have been used as approximations to π in the past. Which is the closest one?

A) 3
B) 3.14
C) 22/7
D) 4
E) Square root of 10

[Answer: C]

7. PHONE TAG

iStock

When Expii's founding team registered the organization in the United States, they needed to select a telephone number. As math enthusiasts, they claimed pi in the new 844 toll-free area code. What is Expii's seven-digit telephone number? (Excluding the area code.)

[Answer: 314-1593; in case you forget to round, you get their FAX number!]

8. PI COINCIDENCE

iStock

The number pi is defined to be the ratio circumference/diameter for any circle. We also all know that the area of a circle is pir^2. Is it a sheer coincidence that they are both the same pi, even though one concerns the circumference and one concerns the area? No!

Let's do it for a regular pentagon. It turns out that for the appropriate definition of the "diameter" of a regular pentagon, if we define the number theta to be the ratio of the perimeter/diameter of any regular pentagon, then its area is always thetar^2, where r is half of the diameter. For this to be true, what should be the "diameter" of a regular pentagon?

A) The distance between the farthest corners of the pentagon.
B) The diameter of the largest circle that fits inside the pentagon.
C) The diameter of the smallest circle that fits around the pentagon.
D) The distance from the base to the opposite corner of the pentagon.
E) Other, not easy to describe.
F) It's a trick question.

[Answer: B]

9. WHAT'S IN A NAME?

iStock

"Expii" brings to mind a number of nice words like "experience," "explore," "explain," "expand," "express," and more. The truth behind the name, however, is based on the most beautiful equation in mathematics:

e^pii + 1 = 0

What is (-1)^-i/pi?

Round your answer to the nearest thousandth.

[Answer: Euler's number, also known as e, or 2.718 (rounded off)]

GETTING EXCITED FOR PI DAY

iStock

The Mathematical Association of America was founded in 1915 to promote and celebrate all things mathematical. It has thousands of members, including mathematicians, math educators, and math enthusiasts, and of course they always celebrate Pi Day. The first two problems are by Lafayette College professor Gary Gordon, while the following four have been sprung on the 300,000+ middle and high school students who participate in the association's annual American Mathematics Competitions. Top scorers in these competitions will sometimes go on to compete on the MAA-sponsored Team USA at the IMO.

10. FLIPPING A COIN

iStock

Alice and Bob each have a coin. Suppose Alice flips hers 1000 times, and Bob flips his 999 times. What is the probability that the number of heads Alice flips will be greater than the number Bob flips?

[Answer: 50 percent. Alice must have either more heads or more tails than Bob (since she has one additional flip), but not both. These two possibilities are symmetric, so each has a 50 percent probability.]

11. CUTTING CHEESE

iStock

You are given a cube of cheese (or tofu, for our vegan readers) and a sharp knife. What is the largest number of pieces one may decompose the cube using n straight cuts? You may not rearrange the pieces between cuts!

[Answer: ((n^3)+5n+6)/6). The trick is that the sequence starts 1, 2, 4, 8, 15, so stopping before the fourth cut will give the wrong impression.]

12. BUYING SOCKS

iStock

Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, some $3 a pair, and some $4 a pair. If he bought at least one pair of each kind, how many pairs of $1 socks did Ralph buy?

A) 4
B) 5
C) 6
D) 7
E) 8

[Answer: D]

13. THE COLOR OF MARBLES

iStock

In a bag of marbles, 3/5 of the marbles are blue, and the rest are red. If the number of red marbles is doubled, and the number of blue marbles stays the same, what fraction of the marbles will be red?

A) 2/5
B) 3/7
C) 4/7
D) 3/5
E) 4/5

[Answer: C]

14. SODA CANS

iStock

If one can holds 12 fluid ounces of soda, what's the minimum number of cans required to provide a gallon (128 ounces) of soda?

[Answer: 11 (you can't have a fraction of a can)]

15. CARPET COVERAGE

iStock

How many square yards of carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide?

March 14, the mathematic high holiday known as Pi Day, is right around the corner. To celebrate everyone's favorite irrational number, we've rounded up some gifts to help the math aficionados in your life—the ones who know that pi is the ratio of the circumference of a circle to its diameter—observe Pi Day in proper fashion.

Mental Floss has affiliate relationships with certain retailers and may receive a small percentage of any sale. But we only get commission on items you buy and don't return, so we're only happy if you're happy. Thanks for helping us pay the bills!

If Pi Day passed and you didn't eat a pi pie, did Pi Day even happen? This specially shaped baking pan makes the equivalent volume of a 9-inch round pan, but obviously has more surface area than a standard pan. Pi puns and extra crust? Sounds like a win-win dessert.

Definitely know your audience before gifting this head-scratcher of a clock. For some, the regular mental exercise to figure out the time would be a welcomed brain-teaser. For others, it could be a frustrating distraction. But, we think its namesake—it should be relatively easy to figure out which Albert it's referencing—would be a fan.

Ancient calculators make great toys when it comes to this colorful bead toy aimed at kids 2 and up. But once the young ones hit grade school, this specially marked abacus will help them visualize arithmetic while still seeing the equations listed out.

This coloring book takes nature's best mathematical patterns and turns them into a soothing adult coloring book. Take a break from studying math's interconnected worlds, and just connect pencil to paper for a bit.

This hands-on math game makes learning arithmetic engaging and entertaining, and can help kids 3–6 years old recognize units and solve basic additions and subtractions. These wooden letters come with three free apps that you pair with any iPad and most Samsung and Nexus tablets.

You saw the movie—now delve even deeper into the true stories of Katherine Johnson, Dorothy Vaughan, Mary Jackson, and the other African-American women who worked at NASA as "human computers" during the Space Race. Margot Lee Shetterly's best-seller reveals just how much ground-breaking work these brilliant mathematicians truly did, even while dealing with both gender discrimination and the Jim Crow era. And if you haven't seen the movie, stream it on HBO or purchase it here.